Solve for x
x=\frac{2}{5}=0.4
x=-\frac{2}{5}=-0.4
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25x^{2}-4=0
Divide both sides by 4.
\left(5x-2\right)\left(5x+2\right)=0
Consider 25x^{2}-4. Rewrite 25x^{2}-4 as \left(5x\right)^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).
x=\frac{2}{5} x=-\frac{2}{5}
To find equation solutions, solve 5x-2=0 and 5x+2=0.
100x^{2}=16
Add 16 to both sides. Anything plus zero gives itself.
x^{2}=\frac{16}{100}
Divide both sides by 100.
x^{2}=\frac{4}{25}
Reduce the fraction \frac{16}{100} to lowest terms by extracting and canceling out 4.
x=\frac{2}{5} x=-\frac{2}{5}
Take the square root of both sides of the equation.
100x^{2}-16=0
Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.
x=\frac{0±\sqrt{0^{2}-4\times 100\left(-16\right)}}{2\times 100}
This equation is in standard form: ax^{2}+bx+c=0. Substitute 100 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.
x=\frac{0±\sqrt{-4\times 100\left(-16\right)}}{2\times 100}
Square 0.
x=\frac{0±\sqrt{-400\left(-16\right)}}{2\times 100}
Multiply -4 times 100.
x=\frac{0±\sqrt{6400}}{2\times 100}
Multiply -400 times -16.
x=\frac{0±80}{2\times 100}
Take the square root of 6400.
x=\frac{0±80}{200}
Multiply 2 times 100.
x=\frac{2}{5}
Now solve the equation x=\frac{0±80}{200} when ± is plus. Reduce the fraction \frac{80}{200} to lowest terms by extracting and canceling out 40.
x=-\frac{2}{5}
Now solve the equation x=\frac{0±80}{200} when ± is minus. Reduce the fraction \frac{-80}{200} to lowest terms by extracting and canceling out 40.
x=\frac{2}{5} x=-\frac{2}{5}
The equation is now solved.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}